Acceleration estimation device and vehicle

ABSTRACT

In an acceleration estimation device for estimating acceleration of a vehicle, a Karman filter for constant speed estimates x-direction acceleration offset and z-direction acceleration offset when a motorcycle is stopped and is traveling at a constant speed. An offset corrector corrects an x-direction acceleration and a z-direction acceleration on the basis of an x-direction acceleration offset estimated value and a z-direction acceleration offset estimated value when the motorcycle is accelerated and decelerated. A Karman filter for acceleration/deceleration estimates the pitch angle of a vehicle body on the basis of a wheel speed and the corrected x-direction acceleration and z-direction acceleration when the motorcycle is accelerated and decelerated. An acceleration corrector obtains an X-direction acceleration and a Z-direction acceleration on the basis of the estimated pitch angle and the corrected x-direction acceleration and z-direction acceleration. A vehicle speed operation unit integrates over time the X-direction acceleration to calculate an X-direction speed.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an acceleration estimation device thatestimates vehicle acceleration, and a vehicle including the same.

2. Description of the Background Art

The traveling speed of a vehicle can be calculated on the basis of therotational speeds of its wheels. When the vehicle is rapidlyaccelerated, however, the wheels may be rotated while slipping on a roadsurface. When the vehicle is rapidly decelerated (braked), the wheelsmay be caused to slide on the road surface. In such a case, the speed ofthe vehicle that can be calculated from the rotational speed of thewheels does not coincide with the actual traveling speed of the vehicle.

Therefore, the acceleration of the vehicle is detected using anacceleration sensor, and the detected acceleration is integrated tocalculate the speed of the vehicle.

When the vehicle is rapidly accelerated or decelerated, however, thevehicle body is inclined up and down in a traveling direction bypitching of the vehicle body. That is, the front of the vehicle bodyrises at the time of the rapid acceleration, and lowers at the time ofthe rapid deceleration. Thus, the forward-and-backward acceleration ofthe vehicle that is detected by the acceleration sensor does notaccurately coincide with an acceleration in a traveling direction of thevehicle.

JP 10-104259 A discloses a vehicle longitudinal acceleration estimatingdevice that removes an unnecessary component of an acceleration sensorfor detecting a longitudinal acceleration to calculate an estimatedvalue of the longitudinal acceleration.

In the longitudinal acceleration estimating device disclosed in JP10-104259 A, the change in an output voltage of the acceleration sensoris frequency-analyzed and is classified into changes due to DC offset,changes due to temperature drift, changes due to road conditions,changes due to acceleration/deceleration of the vehicle, and changes dueto pitching of the vehicle body. A Karman filter is used to extract onlya variable component having a higher frequency than a particularfrequency from a detected value of the longitudinal acceleration by theacceleration sensor.

This causes a variable component due to DC offset and a variablecomponent due to temperature drift respectively having low frequenciesto be removed from the detected value of the longitudinal acceleration.As a result, the estimated value of the longitudinal acceleration is notaffected by changes with time and changes in temperature.

In the longitudinal acceleration estimating device disclosed in JP10-104259A, an unnecessary component in a particular frequency band canbe removed from the detected value in the acceleration sensor.Consequently, it is considered that only a variation component in theparticular frequency band is removed from the detected value in theacceleration sensor to remove the variation component due to pitching ofthe vehicle body.

However, a variation component due to pitching in a frequency band otherthan the particular frequency band cannot be removed. Therefore, thelongitudinal acceleration of the vehicle cannot be accurately estimatedwhen the vehicle is accelerated and decelerated.

On the other hand, JP 8-268257A discloses an actual speed estimator thatestimates an actual vehicle speed of a vehicle. In the actual speedestimator, a coefficient of rolling rigidity and a coefficient ofpitching rigidity are defined to correct an output of a crosswiseacceleration sensor and an output of a lengthwise acceleration sensorusing the coefficient of rolling rigidity and the coefficient ofpitching rigidity.

However, the variation in a pitch angle at the time of the accelerationand deceleration of the vehicle is not constant. In the actual speedestimator disclosed in JP 8-268257 A, the relationship between theoutput of the lengthwise acceleration sensor and the pitch angle isdetermined by the coefficient of pitching rigidity. Therefore, theacceleration in a traveling direction of the vehicle cannot beaccurately estimated in correspondence with arbitrary pitching of thevehicle.

SUMMARY OF THE INVENTION

In order to overcome the problems described above, preferred embodimentsof the present invention provide an acceleration estimation device thatcan accurately estimate an acceleration in a traveling direction of avehicle, and a vehicle including the same.

According to a preferred embodiment of the present invention, anacceleration estimation device for estimating accelerations of a vehicleincludes a first acceleration sensor that is provided in the vehicle anddetects the acceleration in the forward-and-backward direction of thevehicle; a second acceleration sensor that is provided in the vehicleand detects the acceleration in the up-and-down direction of thevehicle; a pitch angle estimator that estimates the pitch angle of thevehicle on the basis of the relationship between a detected value in thefirst acceleration sensor and a detected value in the secondacceleration sensor; and an acceleration calculator that calculates theacceleration in a traveling direction of the vehicle that isperpendicular or substantially perpendicular to a direction of gravity,on the basis of an estimated value of the pitch angle obtained by thepitch angle estimator, the detected value in the first accelerationsensor, and the detected value in the second acceleration sensor.

In the acceleration estimation device, the first acceleration sensor andthe second acceleration sensor are provided in the vehicle. The firstacceleration sensor detects the acceleration in the forward-and-backwarddirection of the vehicle, and the second acceleration sensor detects theacceleration in the up-and-down direction of the vehicle. The pitchangle estimator estimates the pitch angle of the vehicle on the basis ofthe relationship between the detected value in the first accelerationsensor and the detected value in the second acceleration sensor. Theacceleration in the traveling direction of the vehicle is calculated onthe basis of the estimated value of the pitch angle, the detected valuein the first acceleration sensor, and the detected value in the secondacceleration sensor.

In such a way, the pitch angle due to arbitrary pitching of the vehiclecan be estimated with high accuracy. This allows the acceleration in thetraveling direction of the vehicle to be detected with high accuracy.

The acceleration estimation device may further include a speedcalculator that integrates a calculated value of the acceleration in thetraveling direction obtained by the acceleration calculator, tocalculate a speed in the traveling direction. In this case, the speed inthe traveling direction of the vehicle can be detected with highaccuracy.

The pitch angle estimator may include a first Karman filter thatestimates the pitch angle of the vehicle using the relationship amongthe acceleration in the traveling direction of the vehicle that isperpendicular or substantially perpendicular to the direction ofgravity, the acceleration in a vertical direction parallel orsubstantially parallel to the direction of gravity, the detected valuein the first acceleration sensor, and the detected value in the secondacceleration sensor, and the pitch angle of the vehicle.

In this case, the first Karman filter estimates the pitch angle of thevehicle. Even when the detected value of the acceleration in theforward-and-backward direction and the detected value of theacceleration in the up-and-down direction of the vehicle are affected bygravity due to pitching having an arbitrary frequency, it is possible todetect the pitch angle of the vehicle with high accuracy.

The acceleration estimation device may further include an offsetestimator that estimates offset in the first acceleration sensor andoffset in the second acceleration sensor when the vehicle is at asubstantially constant speed, and a corrector that corrects the detectedvalue in the first acceleration sensor and the detected value in thesecond acceleration sensor on the basis of an estimated value of theoffset in the first acceleration sensor and an estimated value of theoffset in the second acceleration sensor that are obtained by the offsetestimator when the vehicle is accelerated or decelerated, and the pitchangle estimator may estimate the pitch angle of the vehicle on the basisof the relationship between the detected value in the first accelerationsensor and the detected value in the second acceleration sensor that arecorrected by the corrector when the vehicle is accelerated ordecelerated.

The time when the vehicle is at a substantially constant speed refers tothe time when the vehicle is stopped and the time when the rate ofchange in the traveling speed of the vehicle is not more than apredetermined threshold value. The threshold value is in a range ofabout −0.2 m/s² to about +0.2 m/s², for example.

In this case, when the vehicle is at a substantially constant speed, theoffset estimator estimates the offset in the first acceleration sensorand the offset in the second acceleration sensor. The offset in thefirst acceleration sensor and the offset in the second accelerationsensor preferably are not changed in a short time period.

When the vehicle is accelerated or decelerated, the corrector correctsthe detected value in the first acceleration sensor and the detectedvalue in the second acceleration sensor on the basis of the estimatedvalue of the offset in the first acceleration sensor and the estimatedvalue of the offset in the second acceleration sensor that are obtainedwhen the vehicle is at a substantially constant speed. The pitch angleof the vehicle is estimated on the basis of the detected value in thefirst acceleration sensor and the detected value in the secondacceleration sensor that are corrected. This allows the pitch angle ofthe vehicle to be detected with higher accuracy.

The acceleration estimation device may further include a wheel speeddetector that detects a wheel speed of the vehicle, and the offsetestimator may include a second Karman filter that estimates the offsetin the first acceleration sensor and the offset in the secondacceleration sensor using the relationship among the acceleration in thetraveling direction, the acceleration in the vertical direction, thedetected value in the first acceleration sensor, the detected value inthe second acceleration sensor, the speed in the traveling direction,the speed in the vertical direction, the speed of the vehicle obtainedfrom the detected value in the wheel speed detector, and the pitch angleof the vehicle.

In this case, the second Karman filter estimates the offset in the firstacceleration sensor and the offset in the second acceleration sensor.Even when the detected value of the acceleration in theforward-and-backward direction and the detected value of theacceleration in the up-and-down direction are affected by gravity due topitching having an arbitrary frequency, therefore, it is possible tomore accurately estimate the offset in the first acceleration sensor andthe offset in the second acceleration sensor. As a result, the pitchangle of the vehicle can be detected with higher accuracy.

An observed disturbance applied to the first acceleration sensor and thesecond acceleration sensor is removed in the second Karman filter. Thisprevents a control system controlled on the basis of the acceleration inthe traveling direction of the vehicle from being unstable due to theobserved disturbance.

The offset estimator may determine that the vehicle is in asubstantially constant speed state when the rate of change in the wheelspeed detected by the wheel speed detector is not more than apredetermined threshold value, and the pitch angle estimator maydetermine that the vehicle is accelerated or decelerated when the rateof change in the wheel speed detected by the wheel speed detector ishigher than the threshold value.

In this case, it is determined that the vehicle is in the substantiallyconstant speed state when the rate of change in the wheel speed is notmore than the threshold value. The offset estimator estimates the offsetin the first acceleration sensor and the offset in the secondacceleration sensor. Further, it is determined that the vehicle isaccelerated or decelerated when the rate of change in the wheel speed ishigher than the threshold value. The pitch angle estimator estimates thepitch angle of the vehicle.

Even when the vehicle speed is slightly changed, therefore, the offsetin the first acceleration sensor and the offset in the secondacceleration sensor can be detected with high accuracy. As a result, thepitch angle of the vehicle can be detected with higher accuracy when thevehicle is accelerated or decelerated.

According to another preferred embodiment of the present invention, avehicle includes a vehicle body, a wheel provided on the vehicle body,an acceleration estimation device that is provided on the vehicle body,and a controller, wherein the acceleration estimation device includes afirst acceleration sensor that is provided on the vehicle and detectsthe acceleration in the forward-and-backward direction of the vehicle; asecond acceleration sensor that is provided on the vehicle and detectsthe acceleration in the up-and-down direction of the vehicle; a pitchangle estimator that estimates the pitch angle of the vehicle on thebasis of the relationship between a detected value in the firstacceleration sensor and a detected value in the second accelerationsensor; and an acceleration calculator that calculates the accelerationin a traveling direction of the vehicle that is perpendicular orsubstantially perpendicular to a direction of gravity on the basis of anestimated value of the pitch angle obtained by the pitch angleestimator, the detected value in the first acceleration sensor, and thedetected value in the second acceleration sensor, the controllercontrols the rotation of the wheel on the basis of the acceleration inthe traveling direction obtained by the acceleration estimation device.

The acceleration estimation device estimates the pitch angle of thevehicle on the basis of the relationship between the detected value inthe first acceleration sensor and the detected value in the secondacceleration sensor. The acceleration in the traveling direction of thevehicle is calculated on the basis of the estimated value of the pitchangle, the detected value in the first acceleration sensor, and thedetected value in the second acceleration sensor. This allows theacceleration in the traveling direction of the vehicle to be detectedwith high accuracy.

The controller controls the rotation of the wheel on the basis of theacceleration in the traveling direction of the vehicle that is obtainedby the acceleration estimation device.

According to the present preferred embodiment, the pitch angle estimatorestimates the pitch angle of the vehicle on the basis of therelationship between the detected value in the first acceleration sensorand the detected value in the second acceleration sensor. Theacceleration in the traveling direction of the vehicle is calculated onthe basis of the estimated value of the pitch angle, the detected valuein the first acceleration sensor, and the detected value in the secondacceleration sensor.

In such a way, the pitch angle due to arbitrary pitching of the vehiclecan be estimated with high accuracy. This allows the acceleration in thetraveling direction of the vehicle to be detected with high accuracy.

Other features, elements, steps, characteristics, and advantages of thepresent invention will become more apparent from the followingdescription of preferred embodiments of the present invention withreference to the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing the relationship of accelerations receivedby an acceleration sensor at the time of deceleration.

FIG. 2 is a diagram showing the schematic configuration of the overallmotorcycle according to a preferred embodiment of the present invention.

FIG. 3 is a schematic view showing a hydraulic system and an electricalsystem of an ABS.

FIG. 4 is a block diagram showing the configuration of a vehicle speedestimator.

FIG. 5 is a diagram for explaining the relationship between an operationof estimating x-direction acceleration offset and z-directionacceleration offset in the vehicle speed estimator and the change inwheel speed.

FIG. 6 is a flowchart showing the operations of the vehicle speedestimator.

FIG. 7 is a block diagram showing the configuration of an ABS signalprocessor.

FIG. 8 is a diagram showing the relationship between an accelerationoffset true value and an acceleration offset estimated error.

FIG. 9 is a diagram showing the change with time of an accelerationoffset estimated value in the process of estimating acceleration offset.

FIG. 10 is a diagram showing the results of estimation of X-directionacceleration.

FIG. 11 is a diagram showing the results of estimation of a vehiclespeed.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the following preferred embodiments, description is made of anexample in which an acceleration estimation device according to thepresent invention is applied to a motorcycle.

(1) Basic Idea of the Present Preferred Embodiment

First, the relationship of accelerations at the time of deceleration ofa motorcycle comprising an acceleration detection device according tothe present preferred embodiment will be described.

FIG. 1 is a diagram showing the relationship of accelerations receivedby an acceleration sensor at the time of deceleration.

As shown in FIG. 1, when a motorcycle 100 is decelerated by afront-wheel brake, a front suspension contracts, and a rear suspensionexpands. Therefore, the motorcycle 100 is inclined forward in itstraveling direction.

A coordinate system fixed to the ground below the motorcycle 100 istaken as a ground coordinate system, and a coordinate system fixed tothe acceleration sensor attached to the motorcycle 100 is taken as asensor coordinate system.

On the ground coordinate system, a traveling direction of the motorcycle100 (a direction perpendicular or substantially perpendicular togravity) on a horizontal ground surface 600 is defined as anX-direction, and a vertical direction (a direction of gravity) isdefined as a Z-direction. Consequently, the X-direction and theZ-direction on the ground coordinate system are not changed irrespectiveof the posture of the motorcycle 100.

On the sensor coordinate system, a direction of the horizontal axis ofthe motorcycle 100 (a forward-and-backward direction of a vehicle body1) in a case where the motorcycle 100 is in a horizontal state isdefined as an x-direction, and a direction perpendicular orsubstantially perpendicular to the horizontal axis of the motorcycle 100(an up-and-down direction of the vehicle body 1) is defined as az-direction. Consequently, the x-direction and the z-direction on thesensor coordinate system are inclined to the X-direction and theZ-direction on the ground coordinate system by the posture of themotorcycle 100.

Hereinafter, the X-direction on the ground coordinate system is merelyreferred to as an X-direction or a traveling direction, and theZ-direction on the ground coordinate system is referred to as aZ-direction or a vertical direction.

From FIG. 1, an acceleration G_(x) in the x-direction and anacceleration G_(z) in the z-direction on the sensor coordinate systemare respectively expressed by the following equations using anacceleration a_(x) in the X-direction and an acceleration a_(z) in theZ-direction on the ground coordinate system:

G _(x) =a _(x) cos θ_(p) −a _(z) sinθ_(p)  (1)

G _(z) =a _(x) sin θ_(p) +a _(z) cos θ_(p)  (2)

In the foregoing equations (1) and (2), θ_(p) denotes the pitch angle ofthe vehicle body 1.

The motorcycle 100 in the present preferred embodiment is provided withan x-direction acceleration sensor for detecting the acceleration G_(x)in the x-direction of the vehicle body 1 and a z-direction accelerationsensor for detecting the acceleration G_(z) in the z-direction.

The acceleration a_(x) in the X-direction and the acceleration a_(z) inthe Z-direction on the ground coordinate system of the motorcycle 100can be measured by detecting the acceleration G_(x) in the x-directionusing the x-direction acceleration sensor, detecting the accelerationG_(z) in the z-direction using the z-direction acceleration sensor, anddetermining the pitch angle θ_(p).

Generally, offset exists in the acceleration sensor. Here, the offset inthe acceleration sensor refers to a value obtained by expressing adifference between a nominal value of an output voltage of theacceleration sensor at an acceleration of 0 m/s² and a value of anactual output voltage of the acceleration sensor in terms of unit ofacceleration (m/s²).

Hereinafter, offset in the x-direction acceleration sensor is referredto as x-direction acceleration offset, and offset in the z-directionacceleration sensor is referred to as z-direction acceleration offset.

In the present preferred embodiment, the x-direction acceleration offsetand the z-direction acceleration offset are estimated using an extendedKarman filter, described later, when the motorcycle 100 is at asubstantially constant speed.

Here, the time when the motorcycle 100 is at a substantially constantspeed includes the time when the motorcycle 100 is stopped and the timewhen the rate of change in the traveling speed of the motorcycle 100 isnot more than a predetermined threshold value. In the followingdescription, the time when the motorcycle 100 is traveling at a constantspeed and the time when the rate of change in the traveling speed is notmore than a threshold value are merely referred to as the time when themotorcycle 100 is traveling at a constant speed.

When the motorcycle 100 is accelerated and decelerated, the accelerationG_(x) in the x-direction and the acceleration G_(z) in the z-directionare corrected on the basis of respective estimated values of thex-direction acceleration offset and the z-direction acceleration offset,and the pitch angle θ_(p) of the vehicle body 1 is estimated on thebasis of respective corrected values of the acceleration G_(x) in thex-direction and the acceleration G_(z) in the z-direction. Further, theacceleration in the X-direction and the acceleration in the Z-directionof the motorcycle 100 are calculated using an estimated value of thepitch angle θ_(p). Further, the acceleration in the X-direction isintegrated to calculate the speed in the X-direction of the motorcycle100.

(2) Configuration of the Motorcycle

FIG. 2 is a diagram showing the schematic configuration of themotorcycle 100 according to the present preferred embodiment. An ABS(Anti-Lock Brake System), described later, is preferably included in themotorcycle 100.

As shown in FIG. 2, a front wheel 2 is attached to the front of thevehicle body 1 of the motorcycle 100, and a rear wheel 3 is attached tothe rear of the vehicle body 1.

A sensor rotor 4 that rotates with the front wheel 2 is provided at thecenter of the front wheel 2. A front-wheel speed sensor 5 for detectingthe rotational speed of the front wheel 2 is attached to the sensorrotor 4. Further, there is provided a front brake caliper 6 that isbrought into contact with a brake disk of the front wheel 2 for brakingthe front wheel 2.

A sensor rotor 7 that rotates with the rear wheel 3 is provided at thecenter of the rear wheel 3. A rear-wheel speed sensor 8 for detectingthe rotational speed of the rear wheel 3 is attached to the sensor rotor7. Further, there is provided a rear brake caliper 9 that is broughtinto contact with a brake disk of the rear wheel 3 for braking the rearwheel 3.

A handle 11 is arranged so as to be swingable right and left at the topon the front side of the vehicle body 1. The handle 11 is provided witha front brake lever 12 and a warning lamp 13.

A hydraulic unit 10 is provided at the center of the vehicle body 1. Arear brake pedal 14 is provided below the center of the vehicle body 1.An x-direction acceleration sensor 21 and a z-direction accelerationsensor 22 are attached to a position at the center of gravity of thevehicle body 1. As the x-direction acceleration sensor 21 and thez-direction acceleration sensor 22, a two-axis acceleration sensor or athree-axis acceleration sensor for use in detection of inclination, animpact of air bags, a drop of hard disks, etc. can be used.

An electronic control unit (hereinafter abbreviated as ECU) 30 and afail-safe relay 31 are provided at the rear of the vehicle body 1.

(3) Configuration of the ABS

FIG. 3 is a schematic view showing a hydraulic system and an electricalsystem of the ABS.

As shown in FIG. 3, a master cylinder 15 is connected to the front brakelever 12, and the master cylinder 15 is connected to the hydraulic unit10. The master cylinder 15 is provided with a brake switch 17. A mastercylinder 16 is connected to the rear brake pedal 14, and the mastercylinder 16 is connected to the hydraulic unit 10. The master cylinder16 is provided with a brake switch 18.

When a driver operates the front brake lever 12, the master cylinder 15raises the pressure of hydraulic fluid supplied to the front brakecaliper 6 from the hydraulic unit 10. This causes the front brakecaliper 6 to be driven to brake the front wheel 2. At this time, thebrake switch 17 is turned on so that a front-wheel brake signal Bf isfed to the ECU 30.

When the driver operates the rear brake lever 14, the master cylinder 16raises the pressure of hydraulic fluid supplied to the rear brakecaliper 9 from the hydraulic unit 10. This causes the rear brake caliper9 to be driven to brake the rear wheel 3. At this time, the brake switch18 is turned on so that a rear-wheel brake signal Br is fed to the ECU30.

A front-wheel speed signal Rf representing the rotational speed of thefront wheel 2 is fed to the ECU 30 from the front-wheel speed sensor 5provided in the sensor rotor 4 in the front wheel 2. A rear-wheel speedsignal Rr representing the rotational speed of the rear wheel 3 is fedto the ECU 30 from the rear-wheel speed sensor 8 provided in the sensorrotor 7 in the rear wheel 3. Hereinafter, the rotational speed of thefront wheel 2 is referred to as a front wheel speed, and the rotationalspeed of the rear wheel 3 is referred to as a rear wheel speed.

An x-direction acceleration signal Ax representing x-directionacceleration is fed to the ECU 30 from the x-direction accelerationsensor 21. A z-direction acceleration signal Az representing z-directionacceleration is fed to the ECU 30 from the z-direction accelerationsensor 22.

The ECU 30 outputs a motor driving signal MD for driving a motor for ahydraulic pump within the hydraulic unit 10 to the hydraulic unit 10through the fail-safe relay 31 in response to the front-wheel brakesignal Bf or the rear-wheel brake signal Br.

The ECU 30 outputs a reduced pressure signal FP for the front wheels anda reduced pressure signal RP for the rear wheels to the hydraulic unit10 through the fail-safe relay 31 on the basis of the front-wheel speedsignal Rf, the rear-wheel speed signal Rr, the x-direction accelerationsignal Ax, and the z-direction acceleration signal Az.

The hydraulic unit 10 reduces the pressure of hydraulic fluid suppliedto the front brake caliper 6 in response to the reduced pressure signalFP. This causes the braking of the front wheel 2 by the front brakecaliper 6 to be released. Further, the motorcycle 100 reduces thepressure of hydraulic fluid supplied to the rear brake caliper 9 inresponse to the reduced pressure signal RP. This causes the braking ofthe rear wheel 3 by the rear brake caliper 9 to be released.

The fail-safe relay 31 switches the operation of the ABS in thehydraulic unit 10 into a normal braking operation when the ABS fails.When the ABS fails, the warning lamp 13 lights up.

(4) Configuration of the Vehicle Speed Estimator

FIG. 4 is a block diagram showing the configuration of a vehicle speedestimator.

The acceleration estimation device according to the present preferredembodiment is preferably used for a vehicle speed estimator 300 shown inFIG. 4. The vehicle speed estimator 300 includes a speed selector 310, afilter selector 320, a Karman filter 330 for constant speed, a Karmanfilter 340 for acceleration/deceleration, an offset storage 350, anoffset corrector 360, an acceleration corrector 370, and a vehicle speedoperation unit 380. Each of the constituent elements within the vehiclespeed estimator 300 is preferably provided in the ECU 30 shown in FIGS.2 and 3 with an associated program function.

The front-wheel speed signal Rf and the rear-wheel speed signal Rr arerespectively fed to the speed selector 310 from the front-wheel speedsensor 5 and the rear-wheel speed sensor 8, and the x-directionacceleration signal Ax is fed thereto from the x-direction accelerationsensor 21.

The speed selector 310 selects the front-wheel speed signal Rf as avehicle speed when the motorcycle 100 is at a substantially constantspeed (is stopped and is traveling at constant speed). When themotorcycle 100 is accelerated and decelerated, the front wheel speed andthe rear wheel speed are compared with each other on the basis of thefront-wheel speed signal Rf and the rear-wheel speed signal Rr, toselect the smaller one of the front wheel speed and the rear wheel speedas a vehicle speed at the time of the acceleration, while selecting thelarger one of the front wheel speed and the rear wheel speed as avehicle speed at the time of the deceleration. Note that a substantiallyconstant speed state or an accelerated/decelerated state is determinedon the basis of the rate of change in the vehicle speed selected at thetime of the determination. The vehicle speed selected by the speedselector 310 is outputted to the vehicle speed operation unit 380.

The vehicle speed is provided to the Karman filter 330 from the speedselector 310, and the x-direction acceleration signal Ax and thez-direction acceleration signal Az are respectively fed from thex-direction acceleration sensor 21 and the z-direction accelerationsensor 22. The Karman filter 330 estimates the x-direction accelerationoffset and the z-direction acceleration offset in a method, describedlater, when the motorcycle 100 is at a substantially constant speed (isstopped and is traveling at a constant speed), to obtain an x-directionacceleration offset estimated value and a z-direction accelerationoffset estimated value.

The offset storage 350 stores the x-direction acceleration offsetestimated value and the z-direction acceleration offset estimated valuethat are obtained by the Karman filter 330.

The x-direction acceleration signal Ax and the z-direction accelerationsignal Az are respectively fed to the offset corrector 360 from thex-direction acceleration sensor 21 and the z-direction accelerationsensor 22, and the x-direction acceleration offset estimated value andthe z-direction acceleration offset estimated value are fed thereto fromthe offset storage 350. The offset corrector 360 corrects thex-direction acceleration and the z-direction acceleration on the basisof the x-direction acceleration offset estimated value, the z-directionacceleration offset estimated value, the x-direction acceleration signalAx, and the z-direction acceleration signal Az when the motorcycle 100is accelerated and decelerated.

The Karman filter 340 estimates the pitch angle of the vehicle body 1 onthe basis of the wheel speed given from the speed selector 310 and thex-direction acceleration and the z-direction acceleration that arecorrected by the offset corrector 360 when the motorcycle 100 isaccelerated and decelerated, to obtain a pitch angle estimated value.

Information representing the results of the determination of thesubstantially constant speed state or the accelerated/decelerated stateis given to the filter selector 320 from the speed selector 310. Basedon the information representing the results of the determination, thefilter selector 320 operates the Karman filter 330 in the substantiallyconstant speed state or operates the Karman filter 340 as well as thevehicle speed operation unit 380 in the accelerated/decelerated state.

The acceleration corrector 370 corrects the x-direction acceleration andthe z-direction acceleration that are corrected by the offset corrector360 on the basis of the pitch angle estimated value obtained by theKarman filter 340 to obtain an X-direction acceleration and aZ-direction acceleration.

The vehicle speed operation unit 380 integrates overtime the X-directionacceleration obtained by the acceleration corrector 370 using thevehicle speed obtained from the speed selector 310 as an initial valueimmediately before the operation to calculate an X-direction speed(vehicle speed) and output a vehicle speed signal VX representing thevehicle speed.

(5) Operation of the Vehicle Speed Estimator

FIG. 5 is a diagram for explaining the relationship between an operationof estimating the x-direction acceleration offset and the z-directionacceleration offset in the vehicle speed estimator 300 and the change inthe wheel speed. In FIG. 5, the vertical axis represents offset andwheel speed, and the horizontal axis represents time. A thick solid lineindicates the change in the wheel speed, and a thin solid line indicatesthe respective changes in the x-direction acceleration offset estimatedvalue and the z-direction acceleration offset estimated value.

The operation of estimating the x-direction acceleration offset and thez-direction acceleration offset is performed in the Karman filter 330for a constant speed when the motorcycle 100 is stopped and is travelingat a constant speed, while the x-direction acceleration offset estimatedvalue and the z-direction acceleration offset estimated value are heldwhen the motorcycle 100 is accelerated and decelerated.

FIG. 6 is a flowchart showing the operations of the vehicle speedestimator 300.

The filter selector 320 in the vehicle speed estimator 300 determineswhether or not the rate of change in a wheel speed selected by the speedselector 310 is larger than a predetermined threshold value (step S1).Here, the threshold value is about −0.2 m/s² to about +0.2 m/s², forexample.

When it is determined in the step S1 that the rate of change in thewheel speed is not more than the predetermined threshold value, thefilter selector 320 considers that the motorcycle 100 is stopped or istraveling at a constant speed to calculate a vehicle speed from thewheel speed (step S2). Here, the vehicle speed corresponds to anX-direction speed observed value, described later.

The Karman filter 330 then respectively estimates offset in thex-direction acceleration sensor 21 (x-direction acceleration offset) andoffset in the z-direction acceleration sensor 22 (z-directionacceleration offset) by a method, described later, to obtain anx-direction acceleration offset estimated value and a z-directionacceleration offset estimated value (step S3). In this case, aZ-direction speed observed value, described later, is taken as zero, forexample. Thereafter, the procedure is returned to the step S1.

When it is determined in the step S1 that the rate of change in thewheel speed is more than the predetermined threshold value, the filterselector 320 considers that the motorcycle 100 is accelerated ordecelerated, and the offset storage 350 stores previous respectivevalues of the x-direction acceleration offset estimated value and thez-direction acceleration offset estimated value (values estimated in thestep S3) (step S4).

The offset corrector 360 then respectively corrects a detected value inthe x-direction acceleration sensor 21 and a detected value in thez-direction acceleration sensor 22 by a method, described later, on thebasis of the x-direction acceleration offset estimated value and thez-direction acceleration offset estimated value that are stored in theoffset storage 350 (step S5).

The Karman filter 340 for acceleration/deceleration then estimates thepitch angle of the vehicle body 1 by a method, described later, on thebasis of the detected value in the x-direction acceleration sensor 21and the detected value in the z-direction acceleration sensor 22 thatare corrected by the offset corrector 360 to obtain a pitch angleestimated value (step S6).

The acceleration corrector 370 then corrects an x-direction accelerationand a z-direction acceleration by a method, described later, using thedetected value in the x-direction acceleration sensor 21 and thedetected value in the z-direction acceleration sensor 22 that arecorrected by the offset corrector 360 and the pitch angle estimatedvalue to calculate an X-direction acceleration and a Y-directionacceleration (step S7).

Furthermore, the vehicle speed operation unit 380 integrates over timethe X-direction acceleration, to calculate a vehicle speed (step S8).Thereafter, the procedure is returned to the step S1.

(6) Configuration and Operation of the ABS Signal Processor

FIG. 7 is a block diagram showing the configuration of an ABS signalprocessor.

The ABS signal processor shown in FIG. 7 includes the vehicle speedestimator 300, a first signal generator 400, and a second signalgenerator 500. The ABS signal processor shown in FIG. 7 is provided inthe ECU 30 shown in FIGS. 2 and 3 with an associated program function.

The first signal generator 400 includes an acceleration operation unit410, a slip determination unit 420, an acceleration determination unit430, and a reduced pressure signal generator 440. The second signalgenerator 500 includes an acceleration operation unit 510, a slipdetermination unit 520, an acceleration determination unit 530, and areduced pressure signal generator 540.

The front-wheel speed signal Rf is fed to the slip determination unit420 in the first signal generator 400 from the front-wheel speed sensor5, and the vehicle speed signal VX is fed thereto from the vehicle speedestimator 300. The front-wheel speed signal Rf is fed to theacceleration operation unit 410 from the front-wheel speed sensor 5.

The slip determination unit 420 determines whether or not the frontwheel 2 is slipping depending on whether or not the difference betweenthe vehicle speed calculated on the basis of the front-wheel speedsignal Rf and the vehicle speed represented by the vehicle speed signalVX is larger than a predetermined reference value.

The acceleration operation unit 410 calculates the acceleration of thefront wheel 2 on the basis of the front-wheel speed signal Rf. Theacceleration determination unit 430 determines whether or not the frontwheel 2 is returned from a slipping state depending on whether or notthe acceleration calculated by the acceleration operation unit 410 ischanged from negative to positive.

The reduced pressure signal generator 440 feeds a reduced pressuresignal FP to the hydraulic unit 10 shown in FIG. 3 when the slipdetermination unit 420 determines that the front wheel 2 is slippingwhile releasing the reduced pressure signal FP when the accelerationdetermination unit 430 determines that the front wheel 2 is returnedfrom a slipping state.

The rear-wheel speed signal Rr is fed to the slip determination unit 520in the second signal generator 500 from the rear-wheel speed sensor 8,and the vehicle speed signal VX is fed thereto from the vehicle speedestimator 300. The rear-wheel speed signal Rr is fed to the accelerationoperation unit 510 from the rear-wheel speed sensor 8.

The slip determination unit 520 determines whether or not the rear wheel3 is slipping depending on whether or not the difference between thevehicle speed calculated on the basis of the rear-wheel speed signal Rrand the vehicle speed represented by the vehicle speed signal VX islarger than a predetermined reference value.

The acceleration operation unit 510 calculates the acceleration of therear wheel 3 on the basis of the rear-wheel speed signal Rr. Theacceleration determination unit 530 determines whether or not the rearwheel 3 is returned from a slipping state depending on whether or notthe acceleration calculated by the acceleration operation unit 510 ischanged from negative to positive.

The reduced pressure signal generator 540 feeds a reduced pressuresignal RP to the hydraulic unit 10 shown in FIG. 3 when the slipdetermination unit 520 determines that the rear wheel 3 is slippingwhile releasing the reduced pressure signal RP when the accelerationdetermination unit 530 determines that the rear wheel 3 is returned froma slipping state.

(7) Estimation of Offset by Karman Filter 330 for Constant Speed

A method of estimating x-direction acceleration offset and z-directionacceleration offset by the Karman filter 330 will now be described.

Considering x-direction acceleration offset, z-direction accelerationoffset, observed noise, and process noise, the following equation of astate is obtained (k is a step in discrete time).

$\begin{matrix}{{Equation}\mspace{20mu} 3} & \; \\{\begin{bmatrix}{V_{x}\left( {k + 1} \right)} \\{a_{x}\left( {k + 1} \right)} \\{ɛ_{offx}\left( {k + 1} \right)} \\{V_{z}\left( {k + 1} \right)} \\{a_{z}\left( {k + 1} \right)} \\{ɛ_{offz}\left( {k + 1} \right)}\end{bmatrix} = {{\begin{bmatrix}1 & T & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & T & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}\left\lbrack \begin{matrix}{V_{x}(k)} \\{a_{x}(k)} \\{ɛ_{offx}(k)} \\{V_{z}(k)} \\{a_{z}(k)} \\{ɛ_{offz}(k)}\end{matrix} \right\rbrack} + \begin{bmatrix}{V_{npx}(k)} \\{a_{npx}(k)} \\{ɛ_{npoffx}(k)} \\{V_{npz}(k)} \\{a_{npz}(k)} \\{ɛ_{npoffz}(k)}\end{bmatrix} + \left\lbrack \begin{matrix}0 \\0 \\0 \\{{- 9.8}T} \\0 \\0\end{matrix} \right\rbrack}} & (3)\end{matrix}$

An observation equation is expressed by the following equation:

$\begin{matrix}{{Equation}\mspace{20mu} 4} & \; \\{\begin{bmatrix}{V_{obx}(k)} \\{G_{obx}(k)} \\{V_{obz}(k)} \\{G_{obz}(k)}\end{bmatrix} = {{\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & {\cos \; {\theta_{p}(k)}} & 1 & 0 & {{- \sin}\; {\theta_{p}(k)}} & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & {\sin \; {\theta_{p}(k)}} & 0 & 0 & {\cos \; {\theta_{p}(k)}} & 1\end{bmatrix}\begin{bmatrix}{V_{x}(k)} \\{a_{x}(k)} \\{ɛ_{offx}(k)} \\{V_{z}(k)} \\{a_{z}(k)} \\{ɛ_{offz}(k)}\end{bmatrix}} + \begin{bmatrix}{V_{nobx}(k)} \\{G_{nobx}(k)} \\{V_{nobz}(k)} \\{G_{nobz}(k)}\end{bmatrix}}} & (4)\end{matrix}$

Elements of the matrix in the foregoing equations (3) and (4) are shownin Table 1.

TABLE 1 V_(x) (k) X-direction Speed [m/s] Ground Coordinate System V_(z)(k) Z-direction Speed [m/s] Ground Coordinate System V_(obx) (k)X-direction Speed Observed Ground Value [m/s] Coordinate System V_(obz)(k) Z-direction Speed Observed Ground Value [m/s] Coordinate Systema_(x) (k) X-direction Acceleration Ground [m/s²] Coordinate System a_(z)(k) Z-direction Acceleration Ground [m/s²] Coordinate System G_(obx) (k)x-direction Acceleration Sensor Observed Value [m/s²] Coordinate SystemG_(obz) (k) z-direction Acceleration Sensor Observed Value [m/s²]Coordinate System ε_(offx) (k) x-direction Acceleration Sensor Offset[m/s²] Coordinate System ε_(offz) (k) z-direction Acceleration SensorOffset [m/s²] Coordinate System θ_(P) (k) Pitch Angle of SensorCoordinate System to Ground Coordinate System [rad] V_(nobx) (k)Observed Noise at Ground X-direction Speed [m/s] Coordinate SystemV_(nobz) (k) Observed Noise at Ground Z-direction Speed [m/s] CoordinateSystem G_(nobx) (k) Observed Noise at Sensor x-direction AccelerationCoordinate System [m/s²] G_(nobz) (k) Observed Noise at Sensorz-direction Acceleration Coordinate System [m/s²] V_(npx) (k) ProcessNoise at Ground X-direction Speed [m/s] Coordinate System V_(npz) (k)Process Noise at Ground Z-direction Speed [m/s] Coordinate Systema_(npx) (k) Process Noise at Ground X-direction Acceleration [m/s²]Coordinate System a_(npz) (k) Process Noise at Ground Z-directionAcceleration [m/s²] Coordinate System ε_(npoffx) (k) Process Noise inX-direction Ground Acceleration Offset [m/s²] Coordinate Systemε_(npoffz) (k) Process Noise in Z-direction Ground Acceleration Offset[m/s²] Coordinate System T Sampling Period [s]

An X-direction speed observed value V_(obx) (k) in the foregoingequation (4) is obtained by the front-wheel speed signal Rf fed from thefront-wheel speed sensor 5 shown in FIG. 4. A Z-direction speed observedvalue V_(obz) (k) is herein set to 0.0 m/s because it is considered tobe almost zero when the motorcycle 100 is stopped and is traveling at aconstant speed.

An x-direction acceleration observed value G_(obx) (k) is obtained bythe x-direction acceleration signal Ax from the x-direction accelerationsensor 21, and a z-direction acceleration observed value G_(obz) (k) isobtained by the z-direction acceleration signal Az from the z-directionacceleration sensor 22.

Values that are actually and empirically valid are respectively set asthe observed noise and the process noise. The observed noise and theprocess noise are adjusted by simulation on the basis of the values.

The left side of the foregoing equation (3) is a state vector x_(k+1) ina step k+1. The state vector x_(k+1) is expressed by the followingequation:

$\begin{matrix}{{Equation}\mspace{20mu} 5} & \; \\{x_{k + 1} = \begin{bmatrix}{V_{x}\left( {k + 1} \right)} \\{a_{x}\left( {k + 1} \right)} \\{ɛ_{offx}\left( {k + 1} \right)} \\{V_{z}\left( {k + 1} \right)} \\{a_{z}\left( {k + 1} \right)} \\{ɛ_{offz}\left( {k + 1} \right)}\end{bmatrix}} & (5)\end{matrix}$

The first term on the right side of the foregoing equation (3) is theproduct of a coefficient vector A and a state vector x_(k) in a step k.The coefficient vector A and the state vector x_(k) are expressed by thefollowing equations:

$\begin{matrix}{{Equation}\mspace{20mu} 6} & \; \\{A = \begin{bmatrix}1 & T & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & T & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}} & (6) \\{{Equation}\mspace{20mu} 7} & \; \\{x_{k} = \begin{bmatrix}{V_{x}(k)} \\{a_{x}(k)} \\{ɛ_{offx}(k)} \\{V_{z}(k)} \\{a_{z}(k)} \\{ɛ_{offz}(k)}\end{bmatrix}} & (7)\end{matrix}$

The second term on the right side of the foregoing equation (3) is aprocess noise vector w_(k) in the step k. The process noise vector w_(k)is expressed by the following equation:

$\begin{matrix}{{Equation}\mspace{20mu} 8} & \; \\{w_{k} = \begin{bmatrix}{V_{npx}(k)} \\{a_{npx}(k)} \\{ɛ_{npoffx}(k)} \\{V_{npz}(k)} \\{a_{npz}(k)} \\{ɛ_{npoffz}(k)}\end{bmatrix}} & (8)\end{matrix}$

The third term on the right side of the foregoing equation (3) is anexternal force vector u_(k) in the step k. The external force vectoru_(k) is expressed by the following equation:

$\begin{matrix}{{Equation}\mspace{20mu} 9} & \; \\{u_{k} = \left\lbrack \begin{matrix}0 \\0 \\0 \\{{- 9.8}T} \\0 \\0\end{matrix} \right\rbrack} & (9)\end{matrix}$

The left side of the foregoing equation (4) is an observation vectory_(k) in the step k. The observation vector y_(k) is expressed by thefollowing equation:

$\begin{matrix}{{Equation}\mspace{20mu} 10} & \; \\{y_{k} = \begin{bmatrix}{V_{obx}(k)} \\{G_{obx}(k)} \\{V_{obz}(k)} \\{G_{obz}(k)}\end{bmatrix}} & (10)\end{matrix}$

The first term on the right side of the foregoing equation (4) is theproduct of a coefficient vector B and the state vector x_(k) in the stepk. The coefficient vector B is expressed by the following equation:

$\begin{matrix}{{Equation}\mspace{20mu} 11} & \; \\{B = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & {\cos \; {\theta_{p}(k)}} & 1 & 0 & {{- \sin}\; {\theta_{p}(k)}} & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & {\sin \; {\theta_{p}(k)}} & 0 & 0 & {\cos \; {\theta_{p}(k)}} & 1\end{bmatrix}} & (11)\end{matrix}$

The second term on the right side of the foregoing equation (4) is anobserved noise vector v_(k) in the step k. The observed noise vectorv_(k) is expressed by the following equation:

$\begin{matrix}{{Equation}\mspace{20mu} 12} & \; \\{v_{k} = \begin{bmatrix}{V_{nobx}(k)} \\{G_{nobx}(k)} \\{V_{nobz}(k)} \\{G_{nobz}(k)}\end{bmatrix}} & (12)\end{matrix}$

From the foregoing equations (5) to (9), the foregoing equation (3) isexpressed by the following equation:

Equation 3a

x _(k+1) =A·x _(k) +w _(k) +u _(k)  (3a)

From the foregoing equations (10) to (12) and (7), the foregoingequation (4) is expressed by the following equation:

Equation 4a

y _(k) =B·x _(k) +v _(k)  (4a)

Here, the x-direction acceleration offset and the z-directionacceleration offset are estimated by sequential calculation using anextended Karman filter in the following manner with a pitch angle θ_(p)included in quantities of state (elements of a state vector).

A state vector z_(k) in the step k, including the pitch angle θ_(p), isexpressed by the following equation:

Equation 13

z _(k) =[x _(k) ^(T)θ_(p)(k)]^(T) =[v _(x)(k)a _(x)(k)ε_(offz)(k)v_(z)(k)a _(z)(k)ε_(offz)(k)|θ_(p)(k)]^(T)  (13)

A subscript T denotes a transported matrix. Further, a functionf_(k)(z_(k)) is expressed by the following equation:

Equation 14

f _(k)(z _(k))=F _(k) z _(k)+[0 0 0 −9.8 T 0 0 |0]^(T)  (14)

In the foregoing equation (14), a coefficient vector F_(k) is expressedby the following equation:

$\begin{matrix}{{Equation}\mspace{20mu} 15} & \; \\{{F_{k} = \begin{bmatrix}1 & T & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & T & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & A_{ax} & 0 & 0 & 0 & 0 & A_{\theta \; p}\end{bmatrix}}{{where},{0 \leq A_{ax} < 1},{0 < A_{\theta \; p} \leq 1}}} & (15)\end{matrix}$

A constant A_(ax) is zero, for example, and a constant A_(θp) is 1, forexample. Here, letting z_(Ek|k) be an estimated value of the statevector z_(k) in the step k, letting z_(Ek|k−1) be an estimated value ofa state vector z_(k) in a step k−1, and letting z_(Ek+1|k) be anestimated value of a state vector z_(k+1) in a step k, a filter equationis expressed by the following equations:

Equation 16

z _(Ek|k) =z _(Ek|k−1) +K _(k)(y _(k) −h _(k)(z _(Ek|k−1)))  (16)

Equation 17

z _(Ek+1|k) =f _(k)(z _(Ek|k))  (17)

In the foregoing equation (16), K_(k) denotes a Karman gain, and theobservation vector y_(k) is expressed by the foregoing equation (10). Afunction h_(k)(z_(Ek|k−1)) will be described later.

The Karman gain K_(k) is expressed by the following equation:

Equation 18

K _(k)Σ_(k|k−1) H _(k) ^(T)(H _(k)Σ_(k|k−1) H _(k) ^(T)+Σ_(vk))⁻¹  (18)

In the foregoing equation (18), Σ_(k|k−1) denotes a covariance matrix ofan estimated error in the state vector z_(k) in the step k−1, and Σ_(vk)denotes a covariance matrix in the observed noise vector v_(k). A matrixH_(k) will be described later.

A covariance matrix Σ_(k|k) of an estimated error in the state vectorz_(k) is expressed by the following equation:

Equation 19

Σ_(k|k)Σ_(k|k−1) −K _(k) H _(k)Σ_(k|k−1)  (19)

A covariance matrix equation of the error is expressed by the followingequation:

Equation 20

Σ_(k+1|k) =F _(k)Σ_(k|k) F _(k) ^(T) +G _(k)Σ_(wk) G _(k) ^(T)  (20)

A matrix G_(k) will be described later. The matrix H_(k) in theforegoing equations (18) and (19) is expressed by the followingequation:

$\begin{matrix}{{Equation}\mspace{20mu} 21} & \; \\{H_{k} = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & {\cos \; {\theta_{p}(k)}} & 1 & 0 & {{- \sin}\; {\theta_{p}(k)}} & 0 & {{{- a_{x}}\sin \; {\theta_{p}(k)}} - {a_{z}\cos \; {\theta_{p}(k)}}} \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & {\sin \; {\theta_{p}(k)}} & 0 & 0 & {\cos \; {\theta_{p}(k)}} & 1 & {{a_{x}\cos \; {\theta_{p}(k)}} - {a_{z}\sin \; {\theta_{p}(k)}}}\end{bmatrix}} & (21)\end{matrix}$

The function h_(k)(z_(Ek|k−1)) in the foregoing equation (16) isexpressed by the following equation:

Equation 22

h _(k)(z _(Ek|k−1))=C _(k)(θ_(pEk|k−1))x _(Ek|k−1)  (22)

In the foregoing equation (22), x_(Ek|k−1) denotes an estimated value ofthe state vector x_(k) in the step k−1. θ_(pEk|k−1) denotes an estimatedvalue of a pitch angle θ_(p) (k) in the step k−1. A matrix C_(k) isexpressed by the following equation:

${{Eq}{uation}}\mspace{14mu} 23\begin{matrix}{C_{k} = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & {\cos \; {\theta_{p}(k)}} & 1 & 0 & {{- \sin}\; {\theta_{p}(k)}} & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & {\sin \; {\theta_{p}(k)}} & 0 & 0 & {\cos \; {\theta_{p}(k)}} & 1\end{bmatrix}} & (23)\end{matrix}$

A matrix G_(k) in the foregoing equation (20) is expressed by thefollowing equation:

$\begin{matrix}{{{Equation}\mspace{14mu} 24}\mspace{79mu} {G_{k} = \begin{bmatrix}I \\0\end{bmatrix}}} & (24)\end{matrix}$

In the foregoing equation (24), I denotes a unit matrix.

The extended Karman filter allows the pitch angle θ_(p) (k), togetherwith x-direction acceleration offset ε_(offx) (k) and z-directionacceleration offset ε_(offz) (k) at the time when the motorcycle 100 isstopped and is traveling at a constant speed, to be estimated.

(8) Simulation of Karman Filter 330 for Constant Speed

Here, the Karman filter 330 was simulated to estimate the x-directionacceleration offset and the z-direction acceleration offset.

FIG. 8 is a diagram showing the relationship between an accelerationoffset true value and an acceleration offset estimated error.

In FIG. 8, the horizontal axis represents respective true values of thex-direction acceleration offset and the z-direction acceleration offset,and the vertical axis represents an estimated error of the accelerationoffset. The estimated error of the acceleration offset is a differencebetween an estimated value of the x-direction acceleration offset andthe true value of the x-direction acceleration offset and a differencebetween an estimated value of the z-direction acceleration offset andthe true value of the z-direction acceleration offset.

In FIG. 8, the estimated error of the z-direction acceleration offset isindicated by a white circle, and the estimated error of the x-directionacceleration offset is indicated by a black triangle. As shown in FIG.8, the estimated error of the x-direction acceleration offset is withinabout 0.06 m/s², and the estimated error of the z-direction accelerationoffset is within about 0.001 m/s².

FIG. 9 is a diagram showing the change with time of an accelerationoffset estimated value in the process of estimating the accelerationoffset.

In FIG. 9, the horizontal axis represents time, and the vertical axisrepresents acceleration offset. In FIG. 9, the true value of thez-direction acceleration offset is indicated by a thin solid line, theestimated value of the z-direction acceleration offset is indicated by athick solid line, the true value of the x-direction acceleration offsetis indicated by a thin dotted line, and the estimated value of thex-direction acceleration offset is indicated by a thick dotted line.

As shown in FIG. 9, both the estimated value of the x-directionacceleration offset and the estimated value of the z-directionacceleration offset are completely converged in two seconds. This allowsthe x-direction acceleration offset and the z-direction accelerationoffset to be estimated if a constant speed state for two or more secondsexists.

(9) Estimation of Pitch Angle by Karman Filter 340 forAcceleration/Deceleration

A method of estimating a pitch angle by the Karman filter 340 will nowbe described.

Considering observed noise and process noise, the following equation ofstate is obtained (k is a step in discrete time).

Equation  25 $\begin{matrix}{\begin{bmatrix}{a_{x}\left( {k + 1} \right)} \\{a_{z}\left( {k + 1} \right)}\end{bmatrix} = {{\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}\begin{bmatrix}{a_{x}(k)} \\{a_{z}(k)}\end{bmatrix}} + \begin{bmatrix}{a_{npx}(k)} \\{a_{npz}(k)}\end{bmatrix}}} & (25)\end{matrix}$

An observation equation is expressed by the following equation.

Equation  26 $\begin{matrix}{\begin{bmatrix}{G_{Aobx}(k)} \\{G_{Aobz}(k)}\end{bmatrix} = {{\begin{bmatrix}{\cos \; {\theta_{p}(k)}} & {{- \sin}\; {\theta_{p}(k)}} \\{\sin \; {\theta_{p}(k)}} & {\cos \; {\theta_{p}(k)}}\end{bmatrix}\begin{bmatrix}{a_{x}(k)} \\{a_{z}(k)}\end{bmatrix}} + \begin{bmatrix}{G_{nobx}(k)} \\{G_{nobz}(k)}\end{bmatrix}}} & (26)\end{matrix}$

Elements of the matrix in the foregoing equations (25) and (26) areshown in Table 2.

TABLE 2 a_(x) (k) X-direction Acceleration Ground [m/s²] CoordinateSystem a_(z) (k) Z-direction Acceleration Ground [m/s²] CoordinateSystem G_(Aobx) (k) x-direction Acceleration Sensor Corrected Value[m/s²] Coordinate System G_(Aobz) (k) z-direction Acceleration SensorCorrected Value [m/s²] Coordinate System θ_(P) (k) Pitch Angle of SensorCoordinate System to Ground Coordinate System [rad] G_(nobx) (k)Observed Noise at Sensor x-direction Acceleration Coordinate System[m/s²] G_(nobz) (k) Observed Noise at Sensor z-direction AccelerationCoordinate System [m/s²] a_(npx) (k) Process Noise at X-direction GroundAcceleration [m/s²] Coordinate System a_(npz) (k) Process Noise atZ-direction Ground Acceleration [m/s²] Coordinate System

Here, an x-direction acceleration corrected value G_(Aobx) (k) is anx-direction acceleration corrected by the offset corrector 360 shown inFIG. 4, and is a value obtained by subtracting the x-directionacceleration offset ε_(offx) (k) from the x-direction accelerationobserved value G_(obx) (k). Further, a z-direction accelerationcorrected value G_(Aobz) (k) is a z-direction acceleration corrected bythe offset corrector 360 shown in FIG. 4, and is a value obtained bysubtracting the z-direction acceleration offset ε_(offz) (k) from thez-direction acceleration observed value G_(obz) (k).

Values that are actually and empirically valid are respectively set asthe observed noise and the process noise. The observed noise and theprocess noise are adjusted by simulation on the basis of the values.

The left side of the foregoing equation (25) is a state vector x_(k+1)in a step k+1. The state vector x_(k+1) is expressed by the followingequation:

Equation  27 $\begin{matrix}{\mspace{79mu} {x_{k + 1} = \begin{bmatrix}{a_{x}\left( {k + 1} \right)} \\{a_{z}\left( {k + 1} \right)}\end{bmatrix}}} & {\mspace{14mu} (27)}\end{matrix}$

The first term on the right side of the foregoing equation (25) is theproduct of a coefficient vector A and a state vector x_(k) in a step k.The coefficient vector A and the state vector x_(k) are expressed by thefollowing equations:

$\begin{matrix}{{{Equation}\mspace{14mu} 28}\mspace{79mu} {A = \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}}} & (28) \\{{{Equation}\mspace{14mu} 29}\mspace{79mu} {x_{k} = \begin{bmatrix}{a_{x}(k)} \\{a_{z}(k)}\end{bmatrix}}} & (29)\end{matrix}$

The second term on the right side of the foregoing equation (25) is aprocess noise vector w_(k) in the step k. The process noise vector w_(k)is expressed by the following equation:

$\begin{matrix}{{{Equation}\mspace{14mu} 30}\mspace{79mu} {w_{k} = \begin{bmatrix}{a_{npx}(k)} \\{a_{npz}(k)}\end{bmatrix}}} & (30)\end{matrix}$

The left side of the foregoing equation (26) is an observation vectory_(k) in the step k. The observation vector y_(k) is expressed by thefollowing equation:

Equation  31 $\; \begin{matrix}{\mspace{79mu} {y_{k} = \begin{bmatrix}{G_{Aobx}(k)} \\{G_{Aobz}(k)}\end{bmatrix}}} & (31)\end{matrix}$

The first term on the right side of the foregoing equation (26) is theproduct of a coefficient vector B and the state vector x_(k) in the stepk. The coefficient vector B is expressed by the following equation:

Equation  32 $\begin{matrix}{\mspace{79mu} {B = \begin{bmatrix}{\cos \; {\theta_{p}(k)}} & {{- \sin}\; {\theta_{p}(k)}} \\{\sin \; {\theta_{p}(k)}} & {\cos \; {\theta_{p}(k)}}\end{bmatrix}}} & (32)\end{matrix}$

The second term on the right side of the foregoing equation (26) is anobserved noise vector v_(k) in the step k. The observed noise vectorv_(k) is expressed by the following equation:

Equation  33 $\begin{matrix}{\mspace{79mu} {v_{k} = \begin{bmatrix}{G_{nobx}(k)} \\{G_{nobz}(k)}\end{bmatrix}}} & (33)\end{matrix}$

From the foregoing equations (27) to (30), the foregoing equation (25)is expressed by the following equation:

Equation 25a

x _(k+1) =A·x _(k) +w _(k)  (25a)

From the foregoing equations (31) to (33) and (29), the foregoingequation (26) is expressed by the following equation:

Equation 26a

y _(k) =B·x _(k) +v _(k)  (25a)

Here, a pitch angle θp is estimated using an extended Karman filter inthe following manner with the pitch angle θ_(p) included in quantitiesof state (elements of a state vector).

A state vector z_(k) in the step k, including the pitch angle θ_(p), isexpressed by the following equation:

Equation 34

z _(k) =[x _(k) ^(T)θ_(p)(k)]^(T) =[a _(x)(k)a_(Z)(k)|θ_(p)(k)]^(T)  (34)

A subscript T denotes a transported matrix. Further, a functionf_(k)(z_(k)) is expressed by the following equation:

Equation 35

f _(k)(z _(k))=F _(k) z _(k)  (35)

In the foregoing equation (35), a coefficient vector F_(k) is expressedby the following equation:

Equation  36 $\begin{matrix}{\mspace{79mu} {{F_{k} = {\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\A_{ax} & 0 & A_{\theta \; p}\end{bmatrix}\mspace{14mu} {where}}},\mspace{79mu} {O \leq A_{ax} < 1},{O < A_{\theta \; p} \leq 1}}} & (36)\end{matrix}$

A constant A_(ax) is zero, for example, and a constant A_(θp) is 1, forexample. Here, letting z_(Ek|k) be an estimated value of the statevector z_(k) in the step k, letting z_(Ek|k−1) be an estimated value ofa state vector z_(k) in a step k−1, and letting z_(Ek+1|k) be anestimated value of a state vector z_(k+1) in a step k, a filter equationis expressed by the following equations:

Equation 37

z _(Ek|k) =z _(Ek|k−1)+K_(k)(y _(k) −h _(Ek|k)))  (37)

Equation 38

z _(Ek+1|+) =f _(k)(z _(Ek|k) ₎  (38)

In the foregoing equation (37), K_(k) denotes a Karman gain, and theobservation vector y_(k) is expressed by the foregoing equation (31). Afunction h_(k)(z_(Ek|k−1)) will be described later.

The Karman gain K_(k) is expressed by the following equation.

Equation 39

K _(k)=Σ_(k|k−1) H _(k) ^(T)(H _(k)Σ_(k|k−1) H _(k) ^(T)+Σ_(vk))⁻¹  (39)

In the foregoing equation (39), Σ_(k|k−1) denotes a covariance matrix ofan estimated error in the state vector z_(k) in the step k−1, and Σ_(vk)denotes a covariance matrix in the observed noise vector v_(k). A matrixH_(k) will be described later.

A covariance matrix z_(k|k) of the estimated error in the state vectorz_(k) is expressed by the following equation:

Equation 40

Σ_(k|k)=Σ_(k|k−1) −K _(k) H _(k)Σ_(k|k−1)  (40)

A covariance matrix equation of the error is expressed by the followingequation:

Equation 41

Σ_(k−1|k) =F _(k)Σ_(k|k) F _(k) ^(T) +G _(k)Σ_(wk) G _(k) ^(T)  (41)

A matrix G_(k) will be described later. The matrix H_(k) is expressed bythe following equation:

Equation  42 $\begin{matrix}{H_{k} = \begin{bmatrix}{\cos \; {\theta_{p}(k)}} & {{- \sin}\; {\theta_{p}(k)}} & {{- a_{x}}\sin \; {\theta_{p}(k)}} & {{- a_{z}}\cos \; {\theta_{p}(k)}} \\{\sin \; {\theta_{p}(k)}} & {\cos \; {\theta_{p}(k)}} & {a_{x}\cos \; {\theta_{p}(k)}} & {{- a_{z}}\sin \; {\theta_{p}(k)}}\end{bmatrix}} & (42)\end{matrix}$

The function h_(k)(z_(Ek|k−1)) in the foregoing equation (37) isexpressed by the following equation:

Equation 43

h _(k)(z _(Ek|k−1))=C _(k)(θ_(pEk|k−1))x _(Ek|k−1)  (43)

In the foregoing equation (43), x_(Ek|k−1) denotes an estimated value ofthe state vector x_(k) in the step k−1. θ_(pEk|k−1) denotes an estimatedvalue of a pitch angle θ_(p) (k) in the step k−1. A matrix C_(k) isexpressed by the following equation:

Equation  44 $\begin{matrix}{\mspace{79mu} {C_{k} = \begin{bmatrix}{\cos \; {\theta_{p}(k)}} & {{- \sin}\; {\theta_{p}(k)}} \\{\sin \; {\theta_{p}(k)}} & {\cos \; {\theta_{p}(k)}}\end{bmatrix}}} & (44)\end{matrix}$

The matrix G_(k) in the foregoing equation (41) is expressed by thefollowing equation:

$\begin{matrix}{{{Equation}\mspace{14mu} 45}\mspace{79mu} {G_{k} = \begin{bmatrix}I \\0\end{bmatrix}}} & (45)\end{matrix}$

In the foregoing equation (45), I denotes a unit matrix.

The extended Karman filter allows the pitch angle θ_(p) (k) at the timewhen the motorcycle 100 is accelerated and decelerated to be estimated.

(10) Correction of Acceleration by Acceleration Corrector 370

The acceleration corrector 370 corrects the x-direction acceleration andthe z-direction acceleration by the following equation using a pitchangle estimated value obtained by the Karman filter 340 foracceleration/deceleration. Thus, an X-direction acceleration estimatedvalue and a Z-direction acceleration estimated value are obtained.

Equation  46 $\begin{matrix}{\mspace{79mu} {\begin{bmatrix}a_{Ex} \\a_{Ez}\end{bmatrix} = {\begin{bmatrix}{\cos \; \theta_{Ep}} & {\sin \; \theta_{Ep}} \\{{- \sin}\; \theta_{Ep}} & {\cos \; \theta_{Ep}}\end{bmatrix}\begin{bmatrix}{G_{Aobx}(k)} \\{G_{Aobz}(k)}\end{bmatrix}}}} & (46)\end{matrix}$

Elements of the matrix in the forgoing equation (46) are shown in Table3.

TABLE 3 a_(Ex) (k) X-direction Acceleration Ground Estimated Value[m/s²] Coordinate System a_(Ez) (k) Z-direction Acceleration GroundEstimated Value [m/s²] Coordinate System G_(Aobx) (k) x-directionAcceleration Sensor Corrected Value [m/s²] Coordinate System G_(Aobz)(k) z-direction Acceleration Sensor Corrected Value [m/s²] CoordinateSystem θ_(Ep) (k) Estimated Value of Pitch Angle of Sensor CoordinateSystem to Ground Coordinate System [rad]

Here, an x-direction acceleration corrected value G_(Aobx) (k) is anx-direction acceleration corrected by the offset corrector 360 shown inFIG. 4, and is a value obtained by subtracting the x-directionacceleration offset ε_(offx) (k) from the x-direction accelerationobserved value G_(obx) (k). Further, a z-direction accelerationcorrected value G_(Aobz) (k) is a z-direction acceleration corrected bythe offset corrector 360 shown in FIG. 4, and is a value obtained bysubtracting the z-direction acceleration offset ε_(offz) (k) from thez-direction acceleration observed value G_(obz) (k).

The foregoing equation (46) allows an x-direction acceleration estimatedvalue a_(Ex) and a Z-direction acceleration estimated value a_(Ez) atthe time when the motorcycle 100 is accelerated and decelerated to becalculated.

(11) Simulation of Karman Filter 340 for Acceleration/Deceleration

Here, the Karman filter 340 and the acceleration corrector 370 weresimulated to estimate the X-direction acceleration and the Z-directionacceleration.

FIG. 10 is a diagram showing the results of the estimation of theX-direction acceleration.

In FIG. 10, the horizontal axis represents time, and the vertical axisrepresents acceleration. In FIG. 10, a true value of the X-directionacceleration is indicated by a dotted line, the X-direction accelerationestimated value a_(Ex) obtained by the acceleration corrector 370 usinga pitch angle estimated value θ_(Ep) obtained by the Karman filter 340is indicated by a solid line, and an x-direction acceleration correctedvalue G_(Aobx) (k) obtained by the offset corrector 360 is indicated bya one-dot and dash line. The x-direction acceleration corrected valueG_(Aobx) (k) is affected by a pitch angle, although the effect of thex-direction acceleration offset is removed therefrom.

As shown in FIG. 10, the X-direction acceleration estimated value a_(Ex)is closer to the true value of the X-direction acceleration, as comparedwith the x-direction acceleration corrected value G_(Aobx) (k).

Furthermore, the true value of the X-direction acceleration, theX-direction acceleration estimated value a_(Ex), and the x-directionacceleration corrected value G_(Aobx) (k) were integrated over time toestimate a vehicle speed.

FIG. 11 is a diagram showing the results of the estimation of thevehicle speed. In FIG. 11, the horizontal axis represents time, and thevertical axis represents a vehicle speed estimated value.

In FIG. 11, a vehicle speed calculated using the true value of theX-direction acceleration (an X-direction vehicle speed true value) isindicated by a dotted line, an X-direction vehicle speed estimated valuecalculated using the X-direction acceleration estimated value a_(Ex) isindicated by a solid line, and an x-direction vehicle speed estimatedvalue calculated using the x-direction acceleration corrected valueG_(Aobx) (k) is indicated by a one-dot and dash line.

As shown in FIG. 11, the X-direction vehicle speed estimated valuecalculated using the X-direction acceleration estimated value a_(Ex) iscloser to the X-direction vehicle speed true value, as compared with thex-direction vehicle speed estimated value calculated using thex-direction acceleration corrected value G_(Aobx) (k).

(12) Effects of the Preferred Embodiments

In the motorcycle 100 according to the present preferred embodiment, theoffset in the x-direction acceleration sensor 21 and the offset in thez-direction acceleration sensor 22 are estimated with high accuracy bythe Karman filter 330 for a constant speed in the vehicle speedestimator 300 when the motorcycle 100 is stopped and is traveling at aconstant speed. Even when the detected value in the x-directionacceleration sensor 21 and the detected value in the z-directionacceleration sensor 22 are affected by gravity due to pitching having anarbitrary frequency, it is possible to accurately estimate the offset inthe x-direction acceleration sensor 21 and the offset in the z-directionacceleration sensor 22.

An observed disturbance given to the x-direction acceleration sensor 21and the z-direction acceleration sensor 22 are removed in the Karmanfilter 330. This prevents the ABS controlled by the vehicle speed in theX-direction obtained by the vehicle speed estimator 300 from beingunstable due to the observed disturbance.

The estimated value of the offset in the x-direction acceleration sensor21 and the estimated value of the offset in the z-direction accelerationsensor 22 that are obtained when the motorcycle 100 is stopped or istraveling at a constant speed are stored in the offset storage 350,while the detected value in the x-direction acceleration sensor 21 andthe detected value in the z-direction acceleration sensor 22 arecorrected by the offset corrector 360 on the basis of the estimatedvalue of the offset in the x-direction acceleration sensor 21 and theestimated value of the offset in the z-direction acceleration sensor 22that are stored in the offset storage 350 when the motorcycle 100 isaccelerated or decelerated. This allows the x-direction acceleration andthe z-direction acceleration of the motorcycle 100 to be detected withhigh accuracy.

The pitch angle of the vehicle body 1 is estimated by the Karman filter340 for acceleration/deceleration when motorcycle 100 is accelerated ordecelerated. This allows the pitch angle due to pitching having anarbitrary frequency to be estimated at low cost and with high accuracywithout using a high-cost gyro sensor.

Furthermore, the X-direction acceleration and the Y-directionacceleration of the motorcycle 100 are calculated by the accelerationcorrector 370 on the basis of the estimated value of the pitch angle,the detected value in the x-direction acceleration sensor 21, and thedetected value in the z-direction acceleration sensor 22. This allowsthe X-direction acceleration of the motorcycle 100 to be detected withhigh accuracy.

The vehicle speed operation unit 380 obtains the vehicle speed in theX-direction from the X-direction acceleration with high accuracy. Whenboth the front wheel 2 and the rear wheel 3 are braked, therefore, it ispossible to detect the sliding of the front wheel 2 and the rear wheel 3as well as to detect the vehicle speed with high accuracy.

In cases where both the front wheel 2 and the rear wheel 3 slide, forexample, a case where the front wheel 2 is braked during the driving ofthe rear wheel 3, the speed at the center of gravity of the vehicle body1 cannot be found from the respective wheel speeds of the front wheel 2and the rear wheel 3. Even in such a case, it is possible to detect thesliding of the front wheel 2 and the rear wheel 3 using the vehiclespeed estimator 300 in the present preferred embodiment as well as todetect the vehicle speed with high accuracy.

(13) Other Preferred Embodiments

Although in the preferred embodiments described above, description wasmade of a case where the acceleration estimation device is applied tothe ABS, the present invention is not limited to this. For example, theacceleration estimation device may be applied to another brake controlsystem, a traction control system, or a cruise control system. Thetraction control system refers to a system for obtaining a driving forcemost suitable for the time of turning, the time of starting, or the timeof acceleration by controlling a driving force of a driving wheel or anoutput of the engine and a braking force. The cruise control systemrefers to a system for automatically controlling a vehicle speed to beconstant in the case of long-distance or long-term traveling.

The acceleration estimation device is also applicable to drivabilitycontrol by an electronic throttle. The drivability control refers to thecontrol for obtaining a comfortable driving performance. When theacceleration estimation device is applied to the drivability control, anerror of an acceleration sensor can be reduced. Therefore, thecomfortable driving performance can be controlled with high accuracy. Asa result, it is possible to provide smooth acceleration characteristicsthat do not make a driver feel changes and variations in acceleration.

Moreover, the acceleration estimation device of the present inventioncan be utilized for estimating the acceleration of a vehicle when a GPS(Global Positioning System) signal cannot be received in a navigationsystem.

Although in the preferred embodiments described above, each of theconstituent elements within the vehicle speed estimator 300 ispreferably provided by the ECU 30 and associated program function, thepresent invention is not limited to this. For example, parts or all ofthe plurality of constituent elements within the vehicle speed estimator300 may be provided by hardware such as an electronic circuit.

Although in the preferred embodiments described above, the offsetestimator preferably includes the Karman filter 330 for a constant speedcomposed of an extended Karman filter, the present invention is notlimited to this. For example, the offset estimator may be achieved byanother adaptive filtering method. For example, an LMS (Least MeanSquare) adaptive filter or H∞ filtering may be used.

Although in the preferred embodiments described above, the pitch angleestimator preferably includes the Karman filter 340 foracceleration/deceleration composed of an extended Karman filter, thepresent invention is not limited to this. For example, the pitch angleestimator may be achieved by another adaptive filtering method. Forexample, an LMS adaptive filter or H∞ filtering may be used.

The vehicle speed estimator 300 in the preferred embodiments describedabove is not limited to the motorcycle 100. For example, it can beapplied to various types of vehicles such as motorcycles, four-wheeledvehicles, and three-wheeled vehicles, or any other suitable vehicle.

While preferred embodiments of the present invention have been describedabove, it is to be understood that variations and modifications will beapparent to those skilled in the art without departing the scope andspirit of the present invention. The scope of the present invention,therefore, is to be determined solely by the following claims.

1. An acceleration estimation device for estimating acceleration of avehicle, comprising: a first acceleration sensor arranged to detect anacceleration in a forward-and-backward direction of the vehicle; asecond acceleration sensor arranged to detect an acceleration in anup-and-down direction of the vehicle; a pitch angle estimator arrangedto estimate a pitch angle of the vehicle on the basis of a relationshipbetween a detected value in the first acceleration sensor and a detectedvalue in the second acceleration sensor; and an acceleration calculatorarranged to calculate an acceleration in a traveling direction of thevehicle that is substantially perpendicular to a direction of gravity onthe basis of an estimated value of the pitch angle obtained by the pitchangle estimator, the detected value in the first acceleration sensor,and the detected value in the second acceleration sensor.
 2. Theacceleration estimation device according to claim 1, further comprisinga speed calculator arranged to integrate a calculated value of theacceleration in the traveling direction obtained by the accelerationcalculator to calculate a speed in the traveling direction.
 3. Theacceleration estimation device according to claim 1, wherein the pitchangle estimator includes: a first Karman filter arranged to estimate thepitch angle of the vehicle using a relationship among the accelerationin the traveling direction of the vehicle that is substantiallyperpendicular to the direction of gravity, an acceleration in a verticaldirection that is substantially parallel to the direction of gravity,the detected value in the first acceleration sensor, and the detectedvalue in the second acceleration sensor, and the pitch angle of thevehicle.
 4. The acceleration estimation device according to claim 1,further comprising: an offset estimator arranged to estimate offset inthe first acceleration sensor and offset in the second accelerationsensor when the vehicle is at a substantially constant speed; and acorrector arranged to correct the detected value in the firstacceleration sensor and the detected value in the second accelerationsensor on the basis of an estimated value of the offset in the firstacceleration sensor and an estimated value of the offset in the secondacceleration sensor that are obtained by the offset estimator when thevehicle is accelerated or decelerated; wherein the pitch angle estimatoris arranged to estimate the pitch angle of the vehicle on the basis ofthe relationship between the detected value in the first accelerationsensor and the detected value in the second acceleration sensor that arecorrected by the corrector when the vehicle is accelerated ordecelerated.
 5. The acceleration estimation device according to claim 4,further comprising a wheel speed detector arranged to detect a wheelspeed of the vehicle, and the offset estimator includes: a second Karmanfilter arranged to estimate the offset in the first acceleration sensorand the offset in the second acceleration sensor using a relationshipamong the acceleration in the traveling direction, the acceleration inthe vertical direction, the detected value in the first accelerationsensor, the detected value in the second acceleration sensor, the speedin the traveling direction, the speed in the vertical direction, thespeed of the vehicle obtained from the detected value in the wheel speeddetector, and the pitch angle of the vehicle.
 6. The accelerationestimation device according to claim 4, wherein: the offset estimator isarranged to determine that the vehicle is in a substantially constantspeed state when the rate of change in the wheel speed detected by thewheel speed detector is not more than a predetermined threshold value;and the pitch angle estimator is arranged to determine that the vehicleis accelerated or decelerated when the rate of change in the wheel speeddetected by the wheel speed detector is higher than the threshold value.7. A vehicle comprising: a vehicle body; a wheel provided on the vehiclebody; an acceleration estimation device provided on the vehicle body;and a controller; wherein the acceleration estimation device includes: afirst acceleration sensor on the vehicle and arranged to detect anacceleration in a forward-and-backward direction of the vehicle; asecond acceleration sensor on the vehicle and arranged to detect anacceleration in an up-and-down direction of the vehicle; a pitch angleestimator arranged to estimate a pitch angle of the vehicle on the basisof a relationship between a detected value in the first accelerationsensor and a detected value in the second acceleration sensor; and anacceleration calculator arranged to calculate an acceleration in atraveling direction of the vehicle that is substantially perpendicularto a direction of gravity on the basis of an estimated value of thepitch angle obtained by the pitch angle estimator, the detected value inthe first acceleration sensor, and the detected value in the secondacceleration sensor; and the controller controls the rotation of thewheel on the basis of the acceleration in the traveling directionobtained by the acceleration estimation device.